Mr Miranda was held at Heathrow for nine hours on Sunday, while in transit from Germany to Brazil.
He has launched a legal challenge over the police's use of anti-terror laws to detain him and seize his property.
But Home Secretary Theresa May said the police must act if someone had "highly sensitive stolen information".
Mr Miranda, a 28-year-old Brazilian national, was held at Heathrow on his way from Berlin to Rio de Janeiro where he lives with Mr Greenwald. The Guardian said he had been carrying "journalistic materials" but was not an employee of the newspaper.
Mr Greenwald has broken most of the stories about state surveillance based on the leaks from fugitive Edward Snowden, who used to work at the US National Security Agency.
Mr Miranda said he was held in a room and questioned by six agents about his "entire life". They confiscated his laptop, an additional hard drive, two memory sticks, a mobile phone, a smart watch and a video games console, his lawyers said.
He was required to divulge the passwords to his personal computers, phone and encrypted storage devices, they added. (+ video) » | Tuesday, August 20, 2013
